Problem: Rewrite as a simplified fraction. ${0.6\overline{81} = {?}}$
Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 681.8181...\\ 10x &= 6.8181...\end{align*}}$ Subtracting the two equations, we have: ${990x = 675}$ ${x = \dfrac{675}{990}} $ ${x = \dfrac{15}{22}} $